Algebra II
Textbook for Students of Mathematics
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Beschreibung
This book is the second volume of an intensive “Russian-style” two-year undergraduate course in abstract algebra, and introduces readers to the basic algebraic structures – fields, rings, modules, algebras, groups, and categories – and explains the main principles of and methods for working with them.
The course covers substantial areas of advanced combinatorics, geometry, linear and multilinear algebra, representation theory, category theory, commutative algebra, Galois theory, and algebraic geometry – topics that are often overlooked in standard undergraduate courses.
This book is the second volume of an intensive “Russian-style” two-year undergraduate course in abstract algebra, and introduces readers to the basic algebraic structures – fields, rings, modules, algebras, groups, and categories – and explains the main principles of and methods for working with them.
The course covers substantial areas of advanced combinatorics, geometry, linear and multilinear algebra, representation theory, category theory, commutative algebra, Galois theory, and algebraic geometry – topics that are often overlooked in standard undergraduate courses.
This textbook is based on courses the author has conducted at the Independent University of Moscow and at the Faculty of Mathematics in the Higher School of Economics. The main content is complemented by a wealth of exercises for class discussion, some of which include comments and hints, as well as problems for independent study.
Challenging amount of material thoughtfully organized for deep and fast learning Large collection of exercises equipped with hints and a lot of problems for independent solution Simple modern explanation of subjects usually omitted in basic courses, such as representations of the symmetric group, geometry of algebraic varieties, meaty aspects of the category theory etc Includes supplementary material: sn.pub/extras
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Alexey L. Gorodentsev
Themen in »Algebra II«
Fields Rings Modules Groups Linear Algebra Multilinear Algebra Representation Theory
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“This is the second of a two-volume set of books offering a ‘Russian-style’ intensive introduction to abstract algebra. … Each chapter contains both ‘exercises’ that are imbedded in the text, and ‘problems’ that are collected at the end of each chapter. … In summary, this book, like its predecessor, seems to have been written for mathematicians … .” (Mark Hunacek, MAA Reviews, March, 2017)
“This textbook contains fourteen chapters furnished with a lot of examples, counterexamples and numerous exercises, some of which are provided with commentary and hints, as well as problems for independent solution that were assigned as homework. … This textbook is self-contained, well written and recommended to undergraduate, graduate and Ph. D. students and it might be very useful for advanced algebra lectures as well.” (Marek Golasiński, zbMATH, Vol. 1365.13001, 2017)
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